Once her father is on board he calls up May Berriman, an old friend who acted in New York and now owns and operates The Gramercy Arms, a boarding house for actresses. May agrees to take on Peggy as a boarder and gets her an audition with the New York Dramatic Academy.
After a quick trip to New York Peggy is accepted into the academy and soon moves into her new home in the city where she quickly becomes close friends with fellow boarder Amy, a southern girl who has also just arrived to attend the dramatic academy.
On their first day of school they meet Mal, a British boy and aspiring director. He soon introduces the girls to his friend Randy, a song and dance man at local nightclubs. Mal and Randy have written a play but have hit an obstacle; they cannot find a theater to rent. The Broadway theaters are too expensive and the off Broadway theaters are booked years in advance. Peggy, wanting to help the boys and possibly wanting to impress Randy, declares she will find them a theater.
Her plan of attack is to look up every theater license issued since the late 1800's, cross-reference them with a recent phonebook, and visit any that are not accounted for in the hopes that some are lying abandoned or forgotten about.
After a bit of searching Peggy finds one that is located on the fifth floor of a building. The building looks vacant but a ring of the door buzzer brings a surly janitor who insists there is no theater before shooing Peggy away.
Suspicious that crooks have taken up use of the theater Peggy suggests that the group take turns surveilling the theater at night in the hopes they will catch illegal doings so the police will clear out the theater thus leaving it available for Mal and Randy. On the second night while Peggy and Amy wait they witness a truck arriving and boxes being unloaded into the theater under armed guard.
After informing the police it is discovered that hijackers have been storing their stolen loot in the old building. It is freed up and the landlord is so grateful he offers Mal and Randy a ten year lease at a steal of a price. Not only can the boys now put on their play but they also decide to turn a lower floor into a male version of the Gramercy Arms.
I read this as an eBook that I got for free from Project Gutenberg which is where the images in this post come from: Peggy Finds the Theater on Project Gutenberg